Objectives The student will be able to:

1. ObjectivesThe student will be able to: 1. solve compound inequalities. 2. graph the solution sets of compound inequalities.

2. What is the difference between and and or? A B AND means intersection -what do the two items have in common? OR means union -if it is in one item, it is in the solution A B

3. o o ● ● ● o 2 2 2 2 3 3 3 3 4 4 4 4 1) Graph x < 4 and x ≥ 2 a) Graph x < 4 b) Graph x ≥ 2 c) Combine the graphs d) Where do they intersect?

4. o o o ● ● ● 2 2 2 2 2 2 3 3 3 3 3 3 4 4 4 4 4 4 2) Graph x < 2 or x ≥ 4 a) Graph x < 2 b) Graph x ≥ 4 c) Combine the graphs

5. o o -3 -2 -1 Answer Now 3) Which inequalities describe the following graph? • y > -3 or y < -1 • y > -3 and y < -1 • y ≤ -3 or y ≥ -1 • y ≥ -3 and y ≤ -1

6. o o 6 7 8 4) Graph the compound inequality 6 < m < 8 When written this way, it is the same thing as 6 < m AND m < 8 It can be rewritten as m > 6 and m < 8 and graphed as previously shown, however, it is easier to graph everything between 6 and 8!

7. Answer Now 5) Which is equivalent to-3 < y < 5? • y > -3 or y < 5 • y > -3 and y < 5 • y < -3 or y > 5 • y < -3 and y > 5

8. Answer Now 6) Which is equivalent to x > -5 and x ≤ 1? • -5 < x ≤ 1 • -5 > x ≥ 1 • -5 > x ≤ 1 • -5 < x ≥ 1

9. o o o o -6 -6 1 1 -3 -3 4 4 0 0 7 7 7) 2x < -6 and 3x ≥ 12 ● Solve each inequality for x Graph each inequality Combine the graphs Where do they intersect? They do not! x cannot be greater than or equal to 4 and less than -3 No Solution!! ●

10. 8) Graph 3 < 2m – 1 < 9 Remember, when written like this, it is an AND problem! 3 < 2m – 1 AND 2m – 1 < 9 Solve each inequality. Graph the intersection of 2 < m and m < 5. - 5 0 5

11. - 5 0 5 9) Graph x < 2 or x ≥ 4

12. 10) Graph x ≥ -1 or x ≤ 3 The whole line is shaded!!